What are Capacitors in Series and Parallel & Their Examples

There are different kinds of capacitors available, based on the application these are classified into different types. The connection of these capacitors can be done in different ways which are used in a variety of applications. Different connections of capacitors perform like a single capacitor. So the total capacitance of this single capacitor mainly depends on how individual capacitors are connected. So basically there are two simple and common types of connections are there like series connection and parallel connection. By using these connections, the total capacitance can be calculated. There are some connections that can also be associated with the connections of series & parallel combinations. This article discusses an overview of what are capacitors in series and parallel with their examples.

Capacitors in Series and Parallel

A capacitor is mainly used for storing electric energy like electrostatic energy. Once there is a need to enhance more energy to store capacity, then an appropriate capacitor with increased capacitance can be necessary. The designing of a capacitor can be done using two metal plates which are allied in parallel & divided through a dielectric medium such as mica, glass, ceramics, etc.


The dielectric medium gives a non-conducting medium between the two plates & includes an exclusive capability to hold the charge.

Once a voltage source is connected across the plates of a capacitor, then a +Ve charge on a single plate & -Ve charge on the next plate get deposited. Here, the total charge ‘q’ is accumulated can be directly proportional to the voltage source ‘V’.

q = CV

Where ‘C’ is capacitance and its value mainly depends on the physical sizes of the capacitor.

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C = εA/d

Where

‘ε’ = dielectric constant

‘A’ = area of the effective plate

d = space among two plates.

Whenever two or more capacitors are allied in series, then the whole capacitance of these capacitors is low as compared with the capacitance of an individual capacitor. Similarly, whenever capacitors are connected in parallel, then the total capacitance of the capacitors is the sum of the capacitances of individual capacitors. By using this, the expressions of total capacitance in series & parallel are derived. Series & parallel parts within the combination of capacitor connections also identified. And the effective capacitance can be calculated through series and parallel through individual capacitances

Capacitors in Series

When a number of capacitors are connected in series, the voltage applied across the capacitors is ‘V’. When the capacitor’s capacitance is C1, C2…Cn, then corresponding capacitance of capacitors when connected in series is ‘C’. The applied voltage across the capacitors is V1, V2, V3….+Vn, correspondingly.

Capacitors in Series
Capacitors in Series

Thus, V = V1+V2+……..+Vn

The charge supplied from the source through these capacitors is ‘Q’ then

V= Q/C, V1= Q/C1, V2= Q/C2, V3=Q/C3 & Vn = Q.Cn

As the charge transferred in every capacitor and current in the whole series combination of capacitors will be identical and it is considered like ‘Q’.

Now, the above equation of ‘V’ can be written like the following.

Q/C = Q/C1+Q/C2+…Q/Cn

Q[1/C] = Q]1/C1+1/C2+…1/Cn]

1/C = 1/C1+1/C2+1/C3+…1/Cn

Example

Whenever capacitors are connected in series then calculate the capacitance of these capacitors. The series connection of capacitors is shown below. Here the capacitors connected in series are two.

The capacitors in the series formula are Ctotal = C1XC2/C1+C2

The values of the two capacitors are C1= 5F and C2=10F

Ctotal = 5FX10F/5F+10F

50F/15F = 3.33F

Capacitors in Parallel

When the capacitance of a capacitor increases, then the capacitors are connected in parallel when two related plates care connected together. The efficient overlapping region can be added through stable spacing among them and therefore their equal capacitance value turns into double individual capacitance. The capacitor bank is used in different industries that use capacitors in parallel. Once two capacitors are allied in parallel after that the voltage ‘V’ across every capacitor is similar that is Veq = Va = Vb & current ‘ieq’ can be separated into two elements like ‘ ia’ & ‘ ib’.

Capacitors in Parallel
Capacitors in Parallel

i = dq/dt

Substitute the value of ‘q’ in the above equation

= d (CV)/dt

i = C dV/dt + VdC/dt

When the capacitance of a capacitor is constant, then

i = C dV/dt

By applying KCL to the above circuit, then the equation will be

ieq = ia+ib

ieq = Ca dVa/dt + Cb dVb/dt

Veq = Va =Vb

ieq = Ca dVeq/dt + Cb dVeq/dt => (Ca+Cb) dVeq/dt

Finally, we can get the following equation

ieq =Ceq dVeq/dt, here Ceq = Ca+Cb

Therefore, once ‘n’ capacitors are allied in parallel the equal capacitance of the total connection can be given through the below equation that looks like to the corresponding resistance of resistors while connected in series.

Ceq = C1+C2+C3+…+Cn

Example

Whenever capacitors are connected in parallel then calculate the capacitance of these capacitors. The parallel connection of capacitors is shown below. Here the capacitors connected in parallel are two.

The capacitors in the parallel formula are Ctotal = C1+C2+C3

The values of two capacitors are C1= 10F, C2=15F, C3=20F

Ctotal = 10F+15F+20F = 45F

The voltage drop across capacitors in series and parallel will be changed based on the individual capacitance values of capacitors.

Examples

The capacitors in series and parallel examples are discussed below.

Capacitors in Series and Parallel Examples
Capacitors in Series and Parallel Examples

Find the capacitance value of three capacitors connected in the following circuit with the values of C1=5 uF, C2= 5uF and C3 =10uF

The values of capacitors are C1=5 uF, C2= 5uF & C3 =10uF

The following circuit can be built with three capacitors namely C1, C2 & C3

When the capacitors C1 & C2 are connected in series, then the capacitance can be calculated as

1/C = 1/C1 +1/C2

1/C= 1/5 + 1/ 5

1/C= 2/5 => 5/2 = 2.5uF

When the above capacitor ‘C’ can be connected in parallel with capacitor ‘C3’, then the capacitance can be calculated as

C (Total) = C+ C3 = 2.5 + 10 = 12.5 microfarads

Therefore the capacitance value can be calculated depending on the analysis of series as well as parallel connections in the circuit. It can be observed when the capacitance value is reduced in series connection. In parallel connection of the capacitor, the capacitance value can be increased. However, while calculating resistance, it is quite reverse.

Thus, this is all about an overview of capacitors in series and parallel with examples. From the above information, finally, we can conclude that by using series and parallel connections of the capacitors, the capacitance can be calculated. Here is a question for you, what is the unit of a capacitor?

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